“...The gravitational pull of the planet alone might be enough to capture...”
Nope. The velocity involved is a measurable percentage of the speed of light.
Chemical engines + aero braking are not getting you enough deltaV reduction without the object burning up in, bouncing off of, or being crushed like a bug on a windshield by the atmosphere.
I would assume the braking force would have to be roughly equal to the accelerating force, and that it would have to be applied at an optimal time to maximize the approach velocity without endangering the orbit.
But the math probably isn't all that complicated. And assuming there is a "go" engine capable of near-light speeds, there is also a "stop" engine with the same capability. The same engines that propel a commercial airliner are responsible for part of its braking upon landing. It's all a question of what direction their thrust is pointing.